That's the contradiction right there. If you are player 2 and get to move, Player 1 is not rational, because you can always reduce their payoff by picking X.

Note that "each player cares only about maximizing his own payoff". By assumption, player 2 has only a selfish preference, not a sadistic one, so they'll only choose X (or be more likely to choose X) if they expect that to improve their own expected score. If player 1 can credibly expect player 2 to play Y often enough when given the opportunity, it is not irrational for player 1 to give player 2 that opportunity by playing B or C.